`a.`\(A=\dfrac{x\sqrt{x}+1}{x-1}-\dfrac{x-1}{\sqrt{x}+1}\) ; \(\left(x\ge0;x\ne1\right)\)
\(A=\dfrac{\left(x\sqrt{x}+1\right)-\left(x-1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(A=\dfrac{x\sqrt{x}+1-x\sqrt{x}+x+\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(A=\dfrac{x+\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(A=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(A=\dfrac{\sqrt{x}}{\sqrt{x}-1}\)
`b.`\(x=2021+2\sqrt{2020}\)
\(\Leftrightarrow x=2020+2\sqrt{2020}+1\)
`<=>`\(x=\left(\sqrt{2020}+1\right)^2\)
\(\Rightarrow A-1=\dfrac{\sqrt{\left(\sqrt{2020}+1\right)^2}}{\sqrt{\left(\sqrt{2020}+1\right)^2}-1}\)
\(\Leftrightarrow A-1=\dfrac{\sqrt{2020}+1}{\sqrt{2020}}\)
\(\Leftrightarrow A=\dfrac{2\sqrt{2020}+1}{\sqrt{2020}}\)
